Mathematical Model Of Process Research Articles

Numerical study of the influence of temperature data error on the determination of frictional heat generation

Subject of research: determination of the friction torque and functions of the specific intensity of heat generation in system of sliding bearings. The purpose of the study: To develop a method for determining the friction torque in sliding bearings using temperature data. Based on computational experiments, study the influence of errors in temperature data on the solution of the inverse problem. Methods and object of research: A system of sliding bearings made of a polymer composite material on which a rotating shaft rests is considered. A mathematical model of the thermal process in the considered system of friction units is presented, taking into account the spatial distribution of temperature and its change over time. The temperature is measured at several points in each bearing. Frictional heat generation is determined by solving the inverse heat conduction problem from the condition that the measured and calculated temperatures are close. To ensure continuous data processing and determine the friction torque during long-term tests, the inverse problem of determining the friction torque from temperature data is solved at successive short time intervals. Then the resulting solutions are «glued together». The main results of the study: With such a restoration, the discrepancy between the specified and restored functions of the specific intensity of heat generation is 10–15 % with an error level in temperature data of 10 %. The developed algorithm for solving the inverse problem of thermal conductivity can be used to determine the friction torques in real systems of self-lubricating sliding bearings.

Technological line for the production of sunflower cake

BACKGROUND: The results of the study conducted to increase the shelf life of sunflower cake by justifying the optimal operating parameters of the ozonizer in the line of the sunflower cake production are presented. Studies of the processing of sunflower cake with an ozone-air mixture at optimal operating parameters, such as its concentration, the duration of its processing and the intensity of the high-frequency field, have been conducted. AIM: Increasing of the long-term storage of protein feed by improving the basic design parameters of the device for its production. METHODS: Resulting from the conducted theoretical research, the technological line for the protein feed production was developed according to the patent for the invention of the Russian Federation No. 2706188. To determine the optimal operating parameters of the device in the sunflower cake production line, which affect its shelf life, the design of experiment theory was used. RESULTS: A regression equation in coded values, characterizing the effect of the concentration of the ozone-air mixture, the duration of the sunflower cake treatment and the intensity of the high-frequency field on the sunflower cake shelf life, is obtained. The analysis of the obtained mathematical model of the processing process is performed. CONCLUSION: Experimental studies of the developed line for the production of sunflower cake with quality control of its treatment with an ozone-air mixture have shown that the sunflower cake shelf life depends on the ozone-air mixture concentration and the duration of treatment of the sunflower cake, as well as on the intensity of the high-frequency field. At the same time, with a decrease in the ozone-air mixture concentration, the duration of treatment of the sunflower cake and the intensity of the high-frequency field during the treatment increase. In the area of low concentration, increased duration up to 120 s and intensity up to 15250 V/m, the shelf life of the cake increases. It is reasonable to process sunflower cake with the ozone-air mixture to increase its shelf life from 3 to 5.45 months according to the GOST 80-96 using the developed line (patent RF 2706188) at a concentration of 23.03 mg/m3, processing time of 134 s and a high-frequency field strength of 17374 V/m.

The HVAC system engineering method for a new family of unified cabins of combine harvesters

BACKGROUND: Designing a combine harvester cabin climate system is a complex and multi-stage process that includes solving a set of tasks. To solve them, a design engineer must have knowledge and skills in various fields, starting with thermal engineering calculations and ending with experimental research methods and computer modeling, which requires a large amount of intellectual and time resources. Therefore, the task of creating a unified method of engineering of combine harvester cabin HVAC system is highly relevant. AIM: Development of the HVAC system for a unified cabin of a grain harvester and a forage harvester. The designed HVAC system is purposed to create a comfortable microclimate in the cabin of the combine for 2 people in summer and winter operating conditions. METHODS: The methodology of calculation and selection of the combine harvester cabin HVAC system, which includes the development of engineering calculation methods and mathematical modeling of thermodynamic and ventilation processes in the cabin, is considered. RESULTS: The main parameters were determined: heat intakes and heat losses for the grain harvester and forage harvester cabins, which amounted to 2.8 and 2.2 kW for the grain harvester, 2.9 and 2.35 kW for the forage harvester; the required air flow rate supplied to the cabin to ensure a comfortable temperature — 740 m3/h; the percentage of air recirculation regarding the conditions of absence of fogging and creation of excessive pressure in the cabin — 75%; the cooling and heating capacity of the HVAC system, taking into account the operating conditions of the combine, are 7.8 and 6.3 kW respectively. The selection of the main equipment of the HVAC system for a unified cabin for a new family of unified cabins of combines — the BUHLER 1000 MFWD evaporator-heater and the Valeo TM16 compressor are chosen. CONCLUSION: The HVAC system designed in accordance with the presented methodology is capable of ensuring a comfortable cabin air temperature in the range of 22–24 °C at various operating modes of the combine harvester in different regions. In addition, the HVAC system parameters eliminate fogging of the cabin windows and the penetration of dusty air inside due to the created excessive pressure.

Vacuum evaporation coupled with anaerobic digestion for process intensification and ammonia recovery: Model development, validation and scenario analysis

A mathematical model for vacuum evaporation process was developed, which was experimentally validated at different initial pHs and temperatures for ammonia removal from anaerobically digested sludge. Six scenarios were evaluated by combining vacuum evaporation process with anaerobic digestion using anaerobic digestion model 1. These scenarios included a control, a pretreatment by vacuum evaporation, a post-treatment by vacuum evaporation at pH 9, a post-treatment by conventional evaporation (100 °C), an intensification with vacuum-concentrated recycled digestate back to the digester, and a second intensification at pH 9. Results indicated that using the evaporator as post-treatment at pH 9 or for intensification at pH 9 were the most favorable options, recovering more than 76 % of the nitrogen present in influent sludge with no negative effect on methane production. An economic analysis showed that the intensification at pH 9 was cost-neutral, significantly higher than the net present value of the control scenario (–22 M$).

Development of mathematical models of power consumption at coal plants

The object of research is coal enterprises where powerful electrical equipment is used (underground installations up to 3000 kW, tunneling complexes of 500–1500 kW, technological complexes of 6–10/0.4 kV, etc.). The deficit of generated capacities, caused by growing energy consumption, can be reduced by regulating power consumption modes. The relevance of this issue is determined by the need to conduct a research of the electricity consumption system, to determine the qualitative and quantitative characteristics of electricity consumption using mathematical models. The lack of mathematical models makes it difficult to analyze energy intensity and consumption modes of each technological operation in the overall balance of electricity consumption of coal enterprises. The article considers the structure and classification of the main technological groups of energy consumers, the development of mathematical models for each type of load modes, as well as a generalized model of electricity consumption of coal enterprises, with the use of mathematical apparatus of probability theory and mathematical statistics. As a result of the work, mathematical models of the electricity consumption process for the main technological groups and for models of daily electricity consumption of coal enterprises as a whole were developed, and it was also established that technological objects of electricity consumption are divided into three different values, in terms of power consumption modes: constant, uniform and pulse. For each class of consumers their statistical characteristics were obtained. The work results can be applied for managing power consumption modes of coal enterprises

Pulse current stabilizer with digital control for the power supply system of the plasmatron

Purpose. Solution of theoretical and practical problems on providing digital control of a pulse converter using high-speed microprocessor tools in the output current stabilization mode with provision of a specified duration of transient processes caused by an increase in load voltage and output current astaticity, which allows to obtain significant advantages over analog versions. Methodology. Review of literary and patent sources on the subject, theory of pulse automatic control systems, mathematical modeling of processes in pulse current stabilizers in the MATLAB / Simulink software environment and physical prototyping. Findings. A simulation model of an autonomous power supply system based on a converter using soft switching technology of transistors and an arc load is presented. A control law is synthesized and a model of a pulse current stabilizer is developed. A method is proposed and ways are found to control a pulse current stabilizer that provide a given duration of transients and astatism of the output current. A model of a pulse stabilizer with digital control based on a single-crystal computing module is developed and manufactured. The results of the study confirm the achievement of a finite duration of transient processes caused by a step change in the load voltage, close to 3-4 periods of conversion and output current astaticism. It is shown that the use of a pulse stabilizer using a fully digital control circuit has undeniable advantages over analog systems. Originality. The problem of synthesizing a digital controller for a given control time by the method of desired transfer functions for a soft switching operating converter on an arc load is solved. In addition to the given control time, additional quality requirements in the steady state are provided. Practical value.The use of microprocessor technology makes it possible not only to implement complex and new highly efficient control algorithms for a converter operating in the pulse current stabilizer mode, but also to perform additional functions for overload protection, self-diagnostics and telemetry of pulse converters. The use of this same digital device simultaneously for the purpose of controlling a pulse converter will allow to abandon analog PWM controllers and thereby reduce its own energy consumption and weight and size characteristics, increase the reliability of the functioning of pulse converters in power supply systems as a whole.

Simulation and modeling of methylene blue dye removal by an agri-food waste (Peanut shells)

Our study explores the potential of utilizing peanut shells, an abundant and low-cost food waste, as a natural adsorbent for the removal of industrial dyes, specifically methylene blue. We conducted a detailed investigation of the adsorption process, which revealed that it conforms to both Langmuir and Freundlich isotherms, indicating the ability of peanut shells to adsorb methylene blue effectively. To optimize the adsorption yield, we employed a Box-Behnken experimental design. This approach allowed us to assess the impact of several key factors, including the mass of the adsorbent, dye concentration, pH, temperature, stirring rate, and the ionic strength of salts in the solution. The mathematical model and simulation of the adsorption process helped us identify the best conditions for maximizing the dye removal. Our experiments resulted in a maximum adsorption efficiency of 97%, achieved under optimal conditions: 1.5 g of adsorbent, a methylene blue concentration of 40 mg/L, pH 11, temperature of 65°C, 0 mg/L ionic strength, and a stirring rate of 165 rpm. These findings suggest that peanut shells are a viable, eco-friendly alternative for dye removal, offering a sustainable solution for wastewater treatment and contributing to waste reduction.

Human Vision as A Multi-Circuit Mathematical Model of the Automated Control System

Abstract The paper contains a proposal an original, extended mathematical model of an automatic system of human vision reaction to a forcing light pulse. A comprehensive mathematical model of the vision process was proposed in the form of an equation described in the frequency (dynamics) domain. Mathematical modelling of human senses is very important. It enables better integration of automation systems with a human cooperating with them, also as an automation system. This provides the basis for reasoning based on a mathematical model instead of intuitive reasoning about human reactions to visual stimuli. A block diagram of the proposed system with five human reaction paths is given. The following can be distinguished in the scheme: the main track consisting of: the transport delay of the eye reaction, the transport delay of the afferent nerves, the inertia of the brain with a preemptive action, the transport delay of the centrifugal nerves and the inertial and transport delay of the neuromotor system. In addition, the scheme of the system includes four tracks of negative feedback of motor and force reactions: upper eyelid, lower eyelid, pupil and lens. In the proposed model, the components of each path along with their partial mathematical models are given and discussed. For each reaction path, their overall mathematical models are also given. Taking into account the comprehensive models of all five reaction paths, a complete mathematical model of the automatic system of human reaction to a forcing light impulse is proposed. The proposed mathematical model opens up many possibilities for synchronizing it with mathematical models of many mechatronics and automation systems and their research. Optimizing the parameters of this model and its synchronization with specific models of automation systems is difficult and requires many numerical experiments. This approach enables the design of automation systems that are better synchronized with human reactions to existing stimuli and the selection of optimal parameters of their operation already in the design phase. The proposed model allows, for example, accurate determination of difficulty levels in computer games. Another example of the use of the proposed model is the study of human reactions to various situations generated virtually, for example in flight simulators and other similar ones.

Математична модель камери згоряння газотурбінного двигуна, який працює на етанолі

Ethanol is one of the most promising alternative fuels for Ukraine. To convert existing projects of power and cogeneration plants based on gas turbine engines (GTEs) operating on petroleum products and natural gas to ethanol, as well as for their design and performance calculation, it is necessary to have a mathematical model of the working process of GTE combustor. The object of the study is the working process of the GTE combustor fueling on ethanol. The subject of the study is a mathematical model of the working process of GTE combustor fueling on ethanol. The work aims to improve a mathematical model of the working process of a GTE combustor fueling on ethanol by changing the algorithm for calculation of the fuel air ratio, considering thermal dissociation, and a correctly formulated equivalent chemical reaction path of the combustion process. To achieve the aim, the following tasks were solved: based on the use of experimental values of specific isobaric heat capacities of combustion products, which are a function of temperature and pressure, a mathematical model of the working process of the GTE combustor was improved ("simplified" mathematical model); based on the solution of the system of equations of chemical thermodynamics, a mathematical model of the working process of the GTE combustor was developed ("complex" mathematical model); the results of calculation by "simplified" mathematical model of the working process of the GTE combustor were compared with the "complex" one. The following results were obtained: the difference in the calculation of the combustion products' thermodynamic parameters between the developed mathematical models was less than 1.2% for the three modes of the General Electric CF6-80A engine. Conclusion: the "simplified" mathematical model of the working process of the GTE combustor fueling on ethanol was improved. A feature of the model is the implicit consideration of the effect of thermal dissociation and correctly formulated equivalent chemical reaction path of the combustion process by using experimental values of specific isobaric heat capacities of combustion products. This will improve the accuracy of fuel air ratio calculation and other thermodynamic parameters of GTE combustor mathematical models fueling on ethanol, without significantly complicating the model algorithm.

Construction of a mathematical model of turbulent heat and mass transfer processes for the case of electron beam melting of titanium alloy casts

This paper describes a mathematical model built for turbulent heat and mass transfer processes in the case of electron beam melting of titanium alloy ingots. The object of research is the conditions that ensure the quality of ingots. The model makes it possible to calculate the distribution of hydrodynamic flows in the liquid metal and temperature fields in the ingot, to determine the profile of the metal crystallization front, taking into account the interphase transition zones. The model solves the problem of finding the necessary melting regimes of ingots by calculation, in contrast to high-cost natural experiments. The thermal and hydrodynamic processes during the melting of a cylindrical ingot with a diameter of 110 mm of the newest titanium alloy Ti-6Al-7Nb for medical use were calculated and its melting parameters were determined. The small diameter of the ingot significantly facilitates its further machining. The geometry of the two-phase zone of the liquidus-solidus transition, which determines the crystallization front of the metal, was calculated. The position and geometry of this front greatly affects the quality of ingot formation and the concentration of the distribution of alloying elements and the homogeneity of the metal across its volume. A sufficiently flat crystallization front has been obtained, under which the given conditions are ensured. It was found that heat transfer in the liquid phase of the metal is mainly caused by heat and mass transfer due to its movement, and heat and mass transfer significantly depends on the power of the electron beam and its distribution on the surface of the bath. According to the calculated regimes, at the Institute of Electric Welding named after E. O. Paton, the National Academy of Sciences of Ukraine, high-quality ingots for the needs of the medical industry were smelted. The castings are used for the manufacture of light and ultra-strong endoprostheses and implants, which are chemically neutral and biologically and biomechanically compatible with the human body and do not cause rejection.

Hot-Pressing Process of Flat-Pressed Wood-Polymer Composites: Theory and Experiment.

The objective of this research was to develop a mathematical model of the hot-pressing process for making flat-pressed wood-polymer composites (FPWPCs). This model was used to calculate and predict the temperature and time required for FPWPC pressing. The model's performance was analysed using the experimental results of hot pressing FPWPCs. It was found that an increase in the content of wood particles led to a rapid increase in the pressing time. The model and experiment showed that the core temperature of the wood-polymer mat remained nearly constant for the first 20-30 s of the hot-pressing process. After this period, this temperature increased rapidly until it reached 100 °C, after which the rate of increase began to decelerate sharply. This transition was more distinct in FPWPCs with a high wood-particle content, while in those with a high thermoplastic-polymer content, it was smoother. Increasing the pressing temperature contributed to a reduction in the time required to heat the FPWPC, as confirmed by both experimental data and the modelling of the hot-pressing process. A decrease in the predicted density of the FPWPC resulted in a directly proportional increase in the time required to heat the mat. Validation of the mathematical model revealed a mean absolute percentage error (MAPE) of only 2.5%, confirming its high precision and reliability. The developed mathematical model exhibited a high degree of accuracy and can be used for further calculations of the time required for FPWPC pressing, considering variable parameters such as pressing temperature, wood-polymer ratio, mat thickness, and density.

Development of a comprehensive theoretical and experimental methodology for evaluating the parameters of recycling by pyrolysis of plastic based on polycarbonate and polyethylene

The results of thermogravimetric and Fourier transform infrared (FTIR) analysis of polymer composite materials (PCM) based on polyethylene and polycarbonate are presented and compared to the polymers polyethylene and polycarbonate. Empirical data were obtained for mathematical modeling, including the amount of solid residue upon pyrolysis, volatile yield, and ash content of the studied PCMs and polymers. Results of the mathematical modeling of the pyrolysis process at a temperature of 600 °C are presented to quantitatively assess the composition of the pyrolysis gas.

Scientific substantiation of the maximum permissible concentration of the pharmaceutical substance osimertinib mesylate in the air of the working area

Introduction. Osimertinib, a 3rd generation epidermal growth factor receptor tyrosine kinase inhibitor, is currently the only drug registered for the treatment of metastatic non-small cell lung cancer in patients with a positive T790M mutation status. The production of osimertinib mesylate is planned on the territory of the Russian Federation, which necessitates research to substantiate the hygienic standard for the aerosol content of the substance in the air of the working area. Conducting research to substantiate the maximum permissible concentration of a substance requires significant material and time resources, while using the results of preclinical and clinical studies, mathematical modeling of processes, and risk assessment methodology allows for a comprehensive assessment of the substance, while significantly reducing the time and cost of work. The study aims to scientifically substantiate the maximum permissible concentration of the pharmaceutical substance osimertinib mesylate in the air of the working area using data from toxicological studies and mathematical modeling of the effects of the substance on humans in industrial conditions. Materials and methods. The materials used were domestic and international databases, reports, research protocols, scientific articles and monographs containing information on the physico-chemical and toxic properties, pharmacotherapeutic activity of osimertinib. Results. The specialists have conducted hygienic regulation of osimertinib, taking into account data on its toxicity, danger, pharmacotherapeutic activity, side effects, long-term consequences, pharmacokinetic studies and modeling. To substantiate the value of the maximum permissible concentration, the authors used the reference points: an inactive NOEL level of 1 mg/­kg/­day for general toxic effect, established in a 92-day experiment on rats with intragastric administration; the lowest observed level of adverse effects of LOAEL is 0.5 mg/kg/day for general toxic effect, established in a 180-day experiment on dogs with intragastric administration; the level that does not cause adverse effects of NOAEL is 10 mg/kg/day for general toxic effect, established in a 180-day experiment on mice with intragastric administration. Safe concentrations of osimertinib in the air of the work area were evaluated using reference points, including the pharmacological effect and the minimum daily therapeutic dose; toxicokinetic modeling of concentrations of a substance in the human body under production conditions and the level of minimal risk. Limitation. The study is limited to the review of open literature sources describing the toxicological/toxicokinetic characteristics of osimertinib mesylate. Conclusion. The most stringent indicators of safe exposure levels, established on the basis of pharmacological effect and toxicokinetic modeling in dogs, allowed us to recommend 0.005 mg/m3, aerosol, hazard class 1 as the maximum permissible concentration in the air of the working area for osimertinib mesylate. Ethics. This study did not require the conclusion of the Ethics Committee.

Study of the extraction kinetics of flavonoids from the fruits of Sophora japonica L. with sunflower oil

Among the large number of biologically active substances contained in the fruits of Sophora japonica L., the extraction of flavonoids, substances of medium polarity, is particularly important. The process of extracting them with vegetable oil from fruits is quite complicated. The object of research is the kinetics of the process of extracting flavonoids from Sophora japonica L. fruits with sunflower oil. The influence of temperature, duration, and hydraulic modulus on the extraction process, as well as on the derivation of the equation of the mathematical model, is studied. Mathematical modeling methods are used in the research. Processing of experimental data for the study of extraction kinetics in the vegetable oil:vegetable raw material system is carried out using the Statistica statistical package. In order to derive the equation of the mathematical model of the process of extracting flavonoids from Sophora japonica L. with sunflower oil, the influence of temperature, duration and hydromodulus on the process of transition of the target component – flavonoids to the extract – is investigated. A mathematical model of the dependence of flavonoids on the hydromodulus (H=10–25), temperature (t=25–45 °С) and the duration of the extraction process of Sophora japonica L. (τ=2–10 h) is obtained, which makes it possible to calculate the content of flavonoids with an average relative with an error within 5 %. On the basis of the conducted experimental studies, basic technological schemes for obtaining unrefined sunflower oil of increased biological value are developed, which includes the following stages: preparation of raw materials, treatment of prepared raw materials with sunflower oil during dilution and mixing, separation of oil from raw materials by filtering. The proposed technology is promising, as its implementation is possible not only in food industry enterprises, but also in restaurant establishments, as it does not require expensive equipment, additional production premises and special training of personnel. The mathematical models of the extraction process of Sophora japonica L. with unrefined sunflower oil proposed in the work allow to select the extraction parameters with a high degree of probability and offer the consumer flavonoid-enriched sunflower oil of increased biological value.

ПІДВИЩЕННЯ ГАЛЬМІВНОЇ ЗДАТНОСТІ ЛОКОМОТИВА ПРОМИСЛО-ВОГО ТРАНСПОРТУ З УРАХУВАННЯМ ЗУСИЛЬ У ЙОГО ЗЧІПНИХ ПРИСТРОЯХ

Objective: substantiation the rational concept of increasing the braking capacity of the industrial locomotive in transient modes of train movement, taking into account the force factor in its coupling device. Methodology of the work: theoretical studies of the energy from the deformation of the coupling devices of the industrial locomotive in the transient modes of train movement; theoretical studies of excessive coupling of locomotive wheels with rails in the presence of force on the locomotive's coupling device; determination of kinematic and dynamic parameters of the transient mode of train movement. A mathematical model of the train motion transitory process has been developed, it using the example of locomotive braking process, which allows determining the current values of train element velocities, as well as coupling forces, and has a low average discrepancy with the data of the technological calculation of industrial locomotive. Fixed: the force on the coupling device of the locomotive changes with a high frequency. The braking process is conventionally divided into 3 stages, which are characterized by oscillations, stabilization and a drop in clutch force; the energy corresponding to the change in force in the clutch during braking falls on 90.5% of the first and second stages. Taking into account the obtained results, the conceptual adjustment of the force of the coupling of the wheel pairs of the locomotive with the rails at the level of the maximum forces in the coupling device of the locomotive, determined by the simulation results, is adopted. Scientific novelty: improvement of the method of determining the required force of the traction the wheels of locomotive with the rails by taking into account the energy corresponding to the change in the effort in the coupling device of the locomotive during the braking time of the train. Practical value: the development of an improved concept by regulating the force the traction of locomotive wheel pairs with rails in transient modes of train movement, taking into account the energy assessment of the effort in the locomotive's coupling device.

Time scale analysis of enzymatic reduction of uric acid in a microfluidic biomedical device

Time Scale Analysis (TSA) is an investigative tool used in engineering design to identify locations in processes that should be a focus of Process Intensification (PI). Furthermore, TSA points to process variables and parameters that could be used to advance and measure PI improvement. However, TSA cannot suggest any specific design solution to intensify process performance. Instead, design engineers should use their fundamental knowledge and creative intelligence to specify detailed design transformations. TSA will then provide a specific quantitative measure of the improvement. TSA implementation improves an explicitly defined process performance, thus helping achieve process intensification goals. TSA is based on first principles, and it utilizes Characteristic Times (CT) such as diffusion, mean residence, and reaction times to improve an existing process. In this study, we specifically consider microfluidic biomedical devices. To illustrate the genesis of CT and TSA, we start by developing a mathematical model of an enzymatic degradation process in a biomedical device called iCore based on mass, momentum, and kinetic equations. After introducing user-defined scaling parameters, we extract CTs pertinent to the enzymatic degradation of uric acid in this microfluidic biomedical device. Diffusion coefficients, microchannel architectural characteristics, enzyme loading, hydrogel thickness, and characteristic parameters of enzyme kinetics are the parameters and process variables incorporated in this analysis. Finally, we compared the extracted CTs with a COMSOL Multiphysics parametric study to demonstrate how time scale analysis as a design tool and adjusting design parameters, such as diffusion coefficient, hydrogel layer thickness, substrate concentration, and enzyme concentration, can enhance the enzymatic reaction process without a need for complex computational modeling. It is crucial to recognize that pertinent CTs can be determined by understanding the type and nature of the observed process, previous experience, published data, and other foundational engineering design work. There is no need for mathematical modeling and numerical simulations to identify and acknowledge the CTs relevant and essential to the observed process; in this work, we only illustrate the principal origin of CTs via a detailed mathematical model of the process, as previously reported by Jovanovic et al. Therefore, in a routine application of TSA, it is important to remember that mathematical modeling and detailed numerical simulations are not necessary. This is a very comforting fact when TSA is deployed as a tool in higher-level process design functions. The investigations on how best to apply TSA in these higher level design functions such as Process Intensification, scale-up/numbering-up, change of device architecture, change of operating conditions, change of process feed characteristics, change of material physical and chemical properties, parametric optimization of the system for various objective functions, and techno-economic analysis, are yet to be studied and reported.

Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality and symmetry, a weak formulation of differential equations and sparse regression. To illustrate this, we extract a complete system of governing equations of fluid dynamics – the Navier–Stokes equation, the continuity equation and the boundary conditions – as well as the pressure-Poisson and energy equations, from numerical data describing a highly turbulent channel flow in three dimensions. Whether they represent known or unknown physics, relations discovered using this approach take the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects. The proposed approach offers insight into the quality of the data, serving as a useful diagnostic tool. It is also remarkably robust, yielding accurate results for very high noise levels, and should thus be well suited for analysis of experimental data.

Towards a Systemic Concept of the Brain Ishemia Stroke: Monte Carlo Driven in silico Model.

The work proposes a new mathematical model of dynamic processes of a typical spatially heterogeneous biological system, and sets and solves a mathematical problem of modeling the dynamics of the system of neurovascular units of the brain in conditions of ischemic stroke. There is a description of only a small number of mathematical models of stroke in the literature. This model is being studied and a numerical and software implementation of the corresponding mathematical problem is proposed. This work is the first attempt ever aiming to employ a Monte Carlo computational approach for In Silico simulation of the most critical parameters in molecular and cellular pathogenesis of the brain ischemic stroke. In this work, a new mathematical model of the development of ischemic stroke is proposed in the form of a discrete model based on neurovascular units (NVU) as elements. As a result of testing the program with the assignment of empirically selected coefficients, data were obtained on the evolution of the states of the lattice of the cellular automaton of the model for the spread of stroke in a region of the brain tissue. A resulting new theoretical model of the particular pathologically altered biosystem might be taken as a promising tool for further studies in neurology; general pathology and cell biology. For the first time, a mathematical model has been constructed that allows us to represent the spatial dynamics of the development of the affected area in ischemic stroke of the brain, taking into account neurovascular units as single morphofunctional structures.

Research on the process of heat transfer between mobile variable temperature heat source and thermoacoustic plate

The purpose of this paper is to analyze the effects of several easy-to-operate parameters (operating frequency, plate stack length, plate stack position, and amplitude) on the refrigeration performance, to explore the optimization path of thermoacoustic refrigerator, and to provide a design basis for further cost reductions. The heat transfer process between the air mass and the plate was investigated as an object, and the physical and mathematical models of the heat transfer process were established. The gas microcluster moving heat and plate stack temperature difference were taken as the response. Operating frequency, plate position, plate length and gas vibration displacement amplitude were the design factors. The change relationship of the system response under the interaction of factors was analyzed by using the central composite experimental design and the response surface method, and experimental verification was carried out. The results show that the deviation of the predicted model from the experimental data is less than 5.9 % when the operating frequency is in the range of 0 Hz–12 Hz, and that the location of the plate stack is 0.45 from the pressure belly point of the sound field, where the heat of the air mass transfer is the largest.

PERIODIC ATEB-FUNCTIONS AND THE VAN DER POL METHOD FOR CONSTRUCTING SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR OSCILLATIONS MODELS OF ELASTIC BODIES

In the process of operation, the simplest elements (hereinafter elastic bodies) of machines and mechanisms under the influence of external and internal factors carry out complex oscillations ‒ a combination of longitudinal, bending and torsion combinations in various combinations. In general, mathematical models of the process of such complex phenomena in elastic bodies, even for one-dimensional calculation models, are boundary value problems for systems of partial differential equations. A two-dimensional mathematical model of oscillatory processes in a nonlinear elastic body is considered. A method of constructing an analytical solution of the corresponding boundary-value problems for nonlinear partial differential equations is proposed, which is based on the use of Ateba functions, the Van der Pol method, ideas of asymptotic integration, and the principle of single-frequency oscillations. For "undisturbed" analogues of the model equations, single-frequency solutions were obtained in an explicit form, and for "perturbed" ‒ analytical dependences of the basic parameters of the oscillation process on a small perturbation. The dependence of the main frequency of oscillations on the amplitude and non-linearity parameter of elastic properties in the case of single-frequency oscillations of "unperturbed motion" is established. An asymptotic approximation of the solution of the autonomous "perturbed" problem is constructed. Graphs of changes in amplitude and frequency of oscillations depending on the values of the system parameters are given.